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List of Uniform Polychora
This is a list of uniform polychora, plus some of the infinite duoprism and antiduoprism series. As of right now, there are 1849 known uniform polychora, most of which were discovered by Jonathan Bowers and George Olshevsky. The polychora are listed by the categories on Bowers' website. Each of the polychora's corresponding Bowers acronyms are bolded and in parentheses. Category 1: Regulars (plus the Tesseractihemioctachoron) (1-17) Convex Regular Polychora (1-6) *1. Pentachoron (pen) *2. Tesseract (tes) *3. Hexadecachoron (hex) *4. Icositetrachoron (ico) *5. Hecatonicosachoron (hi) *6. Hexacosichoron (ex) Self-Intersecting Regular Polychora (7-16) *7. Faceted hexacosichoron (fix) *8. Great hecatonicosachoron (gohi) *9. Grand hecatonicosachoron (gahi) *10. Small stellated hecatonicosachoron (sishi) *11. Great grand hecatonicosachoron (gaghi) *12. Great stellated hecatonicosachoron (gishi) *13. Grand stellated hecatonicosachoron (gashi) *14. Great faceted hexacosichoron (gofix) *15. Grand hexacosichoron (gax) *16. Great grand stellated hecatonicosachoron (gogishi) Tesseractihemioctachoron (17) *17. Tesseractihemioctachoron (tho) Category 2: Truncates (18-38) Convex Truncates (18-23) *18. Truncated pentachoron (tip) *19. Truncated tesseract (tap) *20. Truncated hexadecachoron (thex) *21. Truncated icositetrachoron (tico) *22. Truncated hecatonicosachoron (thi) *23. Truncated hexacosichoron (tex) Star Truncates (24-29) *24. Truncated faceted hexacosichoron (tiffix) *25. Truncated great hecatonicosachoron (tighi) *26. Truncated grand hecatonicosachoron (taghi) *27. Truncated great grand hecatonicosachoron (tigaghi) *28. Truncated great faceted hexacosichoron (tigfix) *29. Truncated grand hexacosichoron (taggix) Truncated tesseractihemioctachoron (30) *30. Truncated tesseractihemioctachoron (titho) Ditrigonary Truncates (31-33) *31. Truncated small ditrigonary hexacosihecatonicosachoron (tissidtixhi) *32. Truncated ditrigonary dishecatonicosachoron ' '(tidtidohi) *33. Truncated great ditrigonary hexacosihecatonicosachoron (tiggidtixhi) Quasitruncates (34-38) *34. Quasitruncated tesseract (quitit) *35. Quasitruncated small stellated hecatonicosachoron (quit sishi) *36. Quasitruncated great stellated hecatonicosachoron (quit gishi) *37. Quasitruncated grand stellated hecatonicosachoron (quit gashi) *38. Quasitruncated great grand stellated hecatonicosachoron (quit gogishi) Category 3: Triangular Rectates (39-59) Rectified pentachoron regiment (39-41) * 39. Rectified pentachoron (rap) * 40. Facetorectified pentachoron (firp) * 41. Pentintercepted pentachoron (pinnip) Rectified tesseract regiment (42-44) * 42. Rectified tesseract (rit) * 43. Facetorectified tesseract (firt) * 44. Hexadecintercepted tesseract (hinnit) Rectified icositetrachoron regiment (45-47) * 45. Rectified icositetrachoron (rico) * 46. Facetorectified icositetrachoron (frico) * 47. Icositetrintercepted icositetrachoron (ini) Rectified hecatonicosachoron regiment (48-50) * 48. Rectified hecatonicosachoron (rahi) * 49. Facetorecified hecatonicosachoron (fry) * 50. Small hecatonicosintercepted hecatonicosachoron (shinhi) Rectified small stellated hecatonicosachoron regiment (51-53) * 51. Rectified small stellated hecatonicosachoron (rasishi) * 52. Facetorectified small stellated hecatonicosachoron (firsashi) * 53. Hecatonicosintercepted small stellated hecatonicosachoron (hinhi) Rectified great grand hecatonicosachoron regiment (54-56) * 54. Rectified great grand hecatonicosachoron (ragaghi) * 55. Facetorectified great grand hecatonicosachoron (firgaghi) * 56. Medial hecatonicosintercepted great grand hecatonicosachoron (mohiny) Rectified great grand stellated hecatonicosachoron (57-59) * 57. Rectified great grand stellated hecatonicosachoron (rigogishi) * 58. Facetorectified great grand stellated hecatonicosachoron (firgogishi) * 59. Great hecatonicosintercepted great grand stellated hecatonicosachoron (gohiny) Category 4: Icositetrachoron Regiment (4, 60-72) Have Full Icositetrachoric symmetry (4, 60) * 4. [[Icositetrachoron|'Icositetrachoron']]' (ico)' * 60. Icositetrahemicositetrachoron (ihi) Have Full Hexadecachoric symmetry (61-66) * 61. Octahemihexadecachoron (oh) * 62. Small hexadecahemihexadecachoron (shahoh) * 63. Hexadecahemihexadecachoron (huhoh) * 64. Hexadecoctahemihexadecachoron (hohoh) * 65. Octahexadecahemihexadecachoron (ohuhoh) * 66. Great hexadecahemihexadecachoron (ghahoh) Have Full Demitesseractic symmetry (67-72) * 67. Rectified tesseractihemioctachoron (ratho) * 68. Octadishemioctachoron (odho) * 69. Hexadecoctadishemioctachoron (hodho) * 70. Hexadecoctihemihexadekintercepted hemioctachoron (hoh honho) * 71. Disoctidishemioctintercepted hemioctachoron (dod honho) * 72. Disoctahemhexadekintercepted hemioctachoron (doh honho) Category 5: Pentagonal Rectates (73-132) Rectified hexacosachoron regiment (73-87) * 73. Rectified hexacosichoron (rox) * 74. Rectified faceted hexacosichoron (rofix) * 75. Small prismatohecatonicosachoron (sophi) * 76. Small pentagonal retroprismatoverted dishecatonicosachoron (sprapivady) * 77. Facetorectified hexacosichoron (frox) * 78. Retroinverted hexacosihecatonicosachoron (rixhi) * 79. Small retropental hecatonicosachoron (sriphi) * 80. Invertipental hexacosidishecatonicosachoron (ipixady) * 81. Polar facetopental prismatohexacosihecatonicosachoron (lifpipixhi) * 82. Interceptipental hexacosidishecatonicosachoron (nipixady) * 83. Small omnicircumfacetopental triakishecatonicosachoron (som fapathi) * 84. Small omnifacetopental triakishecatonicosachoron (sofapathi) * 85. Small circumfacetopental triakishecatonicosachoron (smiffipathi) * 86. Pental prismatohecatonicosintercepted hecatonicosachoron (paphiny) * 87. Small inverted retropental hecatonicosintercepted dishecatonicosachoron (sirphinady) Rectified great hecatonicosachoron regiment (88-102) * 88. Rectified great hecatonicosachoron (righi) * 89. Rectified grand hecatonicosachoron (raghi) * 90. Pentagramal antiprismatoverted hexacosihecatonicosachoron (papvixhi) * 91. Great pentagonal retroprismatoverted dishecatonicosachoron (giprapivady) * 92. Facetorectified great hecatonicosachoron (froghi) * 93. Retroinverted dishecatonicosachoron (ridhei) * 94. Medial retropental hecatonicosachoron (mriphi) * 95. Small invertipental triakishecatonicosachoron (sipathi) * 96. Polar facetopental hexacosidishecatonicosachoron (lifpixadi) * 97. Small interceptipental triakishecatonicosachoron (sipathi) * 98. Medial omnicircumfacetopental triakishecatonicosachoron (mom fapathi) * 99. Great omnifacetopental triakishecatonicosachoron (gofapathi) * 100. Medial circumfacetopental triakishecatonicosachoron (mim fapathi) * 101. Pental hexacosihecatonicosaintercepted hecatonicosachoron (pixhiny) * 102. Great inverted retropental hecatonicosaintercepted dishecatonicosachoron (girphinady) Rectified great stellated hecatonicosachoron regiment (103-117) * 103. Rectified great stellated hecatonicosachoron (ragishi) * 104. Rectified grand stellated hecatonicosachoron (ragashi) * 105. Small pentagramal antiprismatoverted dishecatonicosachoron (spapivady) * 106. Pentagonal retroprismatoverted hexacosihecatonicosachoron (prap vixhi) * 107. Facetorectified great stellated hecatonicosachoron (frogshi) * 108. Retroinverted hecatonicosahexacosichoron (rihix) * 109. Great retropental hecatonicosachoron (griphi) * 110. Medial invertipental triakishecatonicosachoron (mimpathi) * 111. Small polar facetopental triakishecatonicosachoron (sliffipathi) * 112. Medial interceptipental triakishecatonicosachoron (minnipathi) * 113. Great omnicircumfacetopental triakishecatonicosachoron (gom fapathi) * 114. Omnifacetopental hexacosidishecatonicosachoron (ofapaxady) * 115. Great circumfacetopental triakishecatonicosachoron (gam fipithi) * 116. Small pental dishecatonicosaintercepted hecatonicosachoron (spidhiny) * 117. Inverted retropental hexacosintercepted dishecatonicosachoron (irp xanady) Rectified great faceted hexacosichoron regiment (118-132) * 118. Rectified great faceted hexacosichoron (rigfix) * 119. Rectified grand hexacosichoron (raggix) * 120. Great pentagramal antiprismatoverted dishecatonicosachoron (gippapivady) * 121. Quasiprismatohecatonicosachoron (quiphi) * 122. Facetorectified great faceted hexacosichoron (frogfix) * 123. Retroinverted prismatohecatonicosachoron (ripahi) * 124. Grand retropental hecatonicosachoron (graphi) * 125. Great invertipental triakishecatonicosachoron (gipathi) * 126. Great polar facetopental triakishecatonicosachoron (gliffipathi) * 127. Great interceptipental triakishecatonicosachoron (ganipathi) * 128. Omnicircumfacetopental hexacosidishecatonicosachoron (omfapaxady) * 129. Omnifacetopental prismatohexacosihecatonicosachoron (ofpipixhi) * 130. Circumfacetopental hexacosidishecatonicosachoron (mif pixady) * 131. Great pental dishecatonicosintercepted hecatonicosachoron (gipdohiny) * 132. Inverted retropental prismatointercepted dishecatonicosachoron (irp panady) Category 6: Sphenoverts (133-297) Category 7: Bitruncates (298-306) Category 8: Grombates (307-329) Category 9: Omnitruncates (330-351) Category 10: Prismatorhombates (352-441) * 385. Quasiprismatorhombated grand stellated hecatonicosachoron (quippirgashi) Category 11: Antipodiumverts (442-481) Category 12: Podiumverts (482-511) Category 13: Small prismated tetracontoctachoron and great distetracontoctachoron regiments (512-551) Category 14: Skewverts (552-611) Category 15: Antifrustary distetracontoctachoron regiment (612-664) Category 16: Antifrustic hexacositrishecatonicosachoron regiment (665-763) * 709. Great sphenoretrofrustary trishecatonicosachoron (gwirfthi) Category 17: Small stellated hecatonicosachoron regiment (764-777) * 768. Pentagram prismatic heptacosicosachoron (paphicki, small prismosaurus) * 769. Pentagon prismatic heptacosicosachoron (paphacki, great prismosaurus) Category 18: Ditetrahedrals (778-888) Category 19: Prisms (889-962) * 926. Rhombicosidodecahedral prism (sriddip) * 946. Quasitruncated cuboctahedral prism (quitcope) Category 20: Miscellaneous (962-984, 1846-1849) * 963. Grand antiprism (gap) * 1849. Great ditetragonal spinoduoprism (gidtindip) Category 21: Prismated dishecatonicosachoron regiment (985-1065) Category 22: Great dipentary trishecatonicosachoron regiment (1066-1146) * 1138. Great dipentary trishecatonicosadishecatonicosachoron (gidpathidy) Category 23: Rectified small ditrigonal hexacosihecatonicosachoron regiment (1147-1303) * 1285. Great ditrigonary hexacositetrishecatonicosahexacosichoron (gidtuxthix) Category 24: Small tritrigonal prismatohecatonicosidishexacosachoron regiment (1304-1382) Category 25: Great tritrigonal hexacositrishecatonicosachoron regiment (1383-1461) Category 26: Blends (1462-1473) Category 27: Small disnub dihexacosachoron and great disnub dihexacosachoron regiments (1474-1491) Category 28: Small snubs (1492-1668) * 1581. Small dispinosnub snub prismatosnub pentishecatonicosatetrishexacosichoron (sidansos posphitux, Darth Vader) Category 29: Great snubs (1669-1845) * 1695. Great disnub snub hexishexacosipentishecatonicosachoron (gidsoshaxphi) Category A: Duoprisms There are an infinite number of duoprisms; one for each unordered pair of polygons. Some of these are: * {3,3} - Trigonal duoprism (triddip) * {3,4} - Trigonal-square duoprism (tisdip) * {3,5} - Trigonal-pentagonal duoprism (trapedip) * {3,6} - Trigonal-hexagonal duoprism (thiddip) * ... * {4,4} - Tesseract (tes) * {4,5} - Square-pentagonal duoprism (squipdip) * {4,6} - Square-hexagonal duoprism (shiddip) * ... * {5,5} - Pentagonal duoprism (pedip) * {5,6} - Pentagonal-hexagonal duoprism (phiddip) * ... * {6,6} - Hexagonal duoprism (hiddip) * ... * ... Category B: Antiduoprisms Category:Lists of Shapes Category:4 dimensional Category:Uniform polychora Category:Polychora Category:Uniform polytopes